A branching process approach to level‐ <i>k</i> phylogenetic networks

The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In present work we introduce branching process to their study. This approach appears be new this context. Our main results focus on level-k with n labeled leaves. Although number reticulation vertices such is typically linear n, prove that asymptotic global local shape tree-like a well-defined sense. We show depth large network converges towards Brownian excursion after rescaling by . also establish Benjamini–Schramm convergence novel infinite network.